An earlier post had posed the question: "Does anybody know what is relation between 'T' value calculated by 'wilcox_test' function (coin package) and more common 'W' value?" I found the question interesting and ran the commands in R and SPSS. The W reported by R did not seem to correspond to either Mann-Whitney U, Wilcoxon W or the Z which I have more commonly used. Correction for ties may have affected my results. Can anyone else explain what the reported W is and the relation to the reported T? regards bob ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html |
Bob Green <[hidden email]> writes:
> An earlier post had posed the question: "Does anybody know what is relation > between 'T' value calculated by 'wilcox_test' function (coin package) and > more common 'W' value?" > > I found the question interesting and ran the commands in R and SPSS. The W > reported by R did not seem to correspond to either Mann-Whitney U, > Wilcoxon W or the Z which I have more commonly used. Correction for ties > may have affected my results. > > Can anyone else explain what the reported W is and the relation to the > reported T? Well, it's open source... You could just go check. W is the sum of the ranks in the first group, minus the minimum value it can attain, namely sum(1:n1) == n1*(n1+1)/2. In the tied cases, the actual minimum could be larger. The T would seem to be asymptotically normal > wilcox_test(pd ~ age, data = water_transfer,distribution="asymp") Asymptotic Wilcoxon Mann-Whitney Rank Sum Test data: pd by groups 12-26 Weeks, At term T = -1.2247, p-value = 0.2207 alternative hypothesis: true mu is not equal to 0 > pnorm(-1.2247)*2 [1] 0.2206883 so a good guess at its definition is that it is obtained from W or one of the others by subtracting the mean and dividing with the SD. -- O__ ---- Peter Dalgaard Øster Farimagsgade 5, Entr.B c/ /'_ --- Dept. of Biostatistics PO Box 2099, 1014 Cph. K (*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918 ~~~~~~~~~~ - ([hidden email]) FAX: (+45) 35327907 ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html |
Peter Dalgaard wrote: > Bob Green <[hidden email]> writes: > > >>An earlier post had posed the question: "Does anybody know what is relation >>between 'T' value calculated by 'wilcox_test' function (coin package) and >>more common 'W' value?" >> >>I found the question interesting and ran the commands in R and SPSS. The W >>reported by R did not seem to correspond to either Mann-Whitney U, >>Wilcoxon W or the Z which I have more commonly used. Correction for ties >>may have affected my results. >> >>Can anyone else explain what the reported W is and the relation to the >>reported T? > > > Well, it's open source... You could just go check. > > W is the sum of the ranks in the first group, minus the minimum value > it can attain, namely sum(1:n1) == n1*(n1+1)/2. In the tied cases, the > actual minimum could be larger. > > The T would seem to be asymptotically normal > > >>wilcox_test(pd ~ age, data = water_transfer,distribution="asymp") > > > Asymptotic Wilcoxon Mann-Whitney Rank Sum Test > > data: pd by groups 12-26 Weeks, At term > T = -1.2247, p-value = 0.2207 > alternative hypothesis: true mu is not equal to 0 > > >>pnorm(-1.2247)*2 > > [1] 0.2206883 > > so a good guess at its definition is that it is obtained from W or one > of the others by subtracting the mean and dividing with the SD. > With the SD adjusted for ties, of course. (See, e.g., Conover's book.) Peter Ehlers University of Calgary ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html |
P Ehlers <[hidden email]> writes:
> > so a good guess at its definition is that it is obtained from W or one > > of the others by subtracting the mean and dividing with the SD. > > > > With the SD adjusted for ties, of course. (See, e.g., Conover's book.) ...which is actually the exact SD, conditional on the set of tied ranks, not just a correction term. See my discussion with Torsten a month or so ago. -- O__ ---- Peter Dalgaard Øster Farimagsgade 5, Entr.B c/ /'_ --- Dept. of Biostatistics PO Box 2099, 1014 Cph. K (*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918 ~~~~~~~~~~ - ([hidden email]) FAX: (+45) 35327907 ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html |
On Wed, 21 Dec 2005, Peter Dalgaard wrote: > P Ehlers <[hidden email]> writes: > > > > so a good guess at its definition is that it is obtained from W or one > > > of the others by subtracting the mean and dividing with the SD. > > > > > > > With the SD adjusted for ties, of course. (See, e.g., Conover's book.) > > ...which is actually the exact SD, conditional on the set of tied > ranks, not just a correction term. See my discussion with Torsten a > month or so ago. > yes, exactly. Thanks, Peter! The `T' values reported by functions in the `coin' package are _standardized_ statistics. Standardization is done utilizing the conditional expectation and conditional variance of the underlying linear statistics as given by Strasser & Weber (1999). Note that _no_ `continuity correction' whatsoever is applied. The limit distribution is normal (or chisq, when the test statistic is a quadratic form). The vignette explains the theoretical framework `coin' maps into software in more detail. It _definitively_ is worse the effort to have a look at it. At first glance it might seem a little bit abstract but after this you'll see how general and powerful the tools are. We are currently working on a manuscript showing more applications, so watch out for the new `coin' version in a few days. Best, Torsten > -- > O__ ---- Peter Dalgaard Øster Farimagsgade 5, Entr.B > c/ /'_ --- Dept. of Biostatistics PO Box 2099, 1014 Cph. K > (*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918 > ~~~~~~~~~~ - ([hidden email]) FAX: (+45) 35327907 > > ______________________________________________ > [hidden email] mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html > > ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html |
In reply to this post by Peter Dalgaard
Peter,
You're right, of course, as usual. Sorry about that. Peter E. Peter Dalgaard wrote: > P Ehlers <[hidden email]> writes: > > >>>so a good guess at its definition is that it is obtained from W or one >>>of the others by subtracting the mean and dividing with the SD. >>> >> >>With the SD adjusted for ties, of course. (See, e.g., Conover's book.) > > > ...which is actually the exact SD, conditional on the set of tied > ranks, not just a correction term. See my discussion with Torsten a > month or so ago. > ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html |
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